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If (2 +3 )=2, show that (3 -2 )= 3.

Question

If $(2 sin θ + 3 cos θ) = 2$ , show that $(3 sin θ - 2 cos θ) = \pm 3$ .

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Emma Discussed

If

(2 sin θ + 3 cos θ) = 2

, show that

(3 sin θ - 2 cos θ) = \pm 3

.

9 mins ago

Discuss this question LIVE

9 mins ago

Text solutionVerified

(2 sin θ + 3 cos θ) = 2.... (1)

(2 sin θ + 3 cos θ)^{2} + (3 sin θ - 2 cos θ)^{2}

= 4 sin^{2} θ + 9 cos^{2} θ + 12 sin θ cos θ + 9 sin^{2} θ + 4 cos^{2} θ - 12 sin θ cos θ

= 13 sin^{2} θ + 13 cos^{2} θ

= 13 (sin^{2} θ + cos^{2} θ)

= 13

(Because

(sin^{2} θ + cos^{2} θ) = 1

)

\Rightarrow (2 sin θ + 3 cos θ)^{2} + (3 sin θ - 2 cos θ)^{2} = 13

\Rightarrow (2)^{2} + (3 sin θ - 2 cos θ)^{2} = 9

Using equation

(1)

\Rightarrow (3 sin θ - 2 cos θ)^{2} = 9

or

(3 sin θ - 2 cos θ) = \pm 3

Hence proved.

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Question Text	If $(2 sin θ + 3 cos θ) = 2$ , show that $(3 sin θ - 2 cos θ) = \pm 3$ .
Answer Type	Text solution:1
Upvotes	150